H-D isotope shift in the Balmer series

This repository documents a hydrogen-deuterium isotope-shift measurement carried out with a scanning monochromator and photomultiplier readout. The focus here is the analysis workflow: repeated measurements, calibration-aware uncertainty propagation, and comparison with reduced-mass theory.

Project Overview

This repository shows careful treatment of repeated measurements, calibration terms, and sensitivity to window choices in raw-scan fitting. I keep both the table recomputation script and the optional raw-fit script visible so the repository distinguishes stable reported results from more assumption-sensitive exploratory fits.

At a Glance

• Data workflow: repeated H-D scans and calibration records are reduced into comparison tables, uncertainty budgets, JSON summaries, and diagnostic figures.
• Methods signal: repeated-measurement aggregation, calibration-aware uncertainty propagation, and sensitivity checks for raw fitting windows.
• Reproducibility signal: the main script recomputes the stable Day 4 results, while the raw-fit helper keeps more assumption-sensitive choices separate and visible. The repository separates stable reported results from more assumption-sensitive exploratory fits, so readers can see which outputs are used for the main conclusion.

Authors: Hongyu Wang, Cici Zhang
Advisor: Philip Lubin, Department of Physics, UC Santa Barbara

Research snapshot

Day 4 summary

The final results come from the Day 4 new-lamp dataset, where four repeated scans were recorded for each Balmer line and combined with the quoted scan-rate calibration term.

Line	Experimental Delta lambda (A)	Total uncertainty (A)	Theory (A)	Percent difference
H alpha	1.801	0.052	1.7858	+0.85%
H beta	1.263	0.039	1.3228	-4.52%

H alpha is close to the theoretical value within the quoted total uncertainty. H beta shows the larger deviation and is the more calibration-sensitive result in this dataset.

Analysis figures

Experimental shifts compared with theory

Statistical vs calibration uncertainty

Python analysis workflow

• Recompute the reported Day 4 values from the recorded trial shifts
• Separate statistical scatter from the scan-rate calibration term
• Propagate total uncertainty in quadrature
• Export machine-readable outputs to CSV and JSON
• Optionally refit raw H-D doublets with a two-Gaussian plus linear-baseline model

The main reproducible script is analysis/recompute_tables_day4.py. It regenerates the comparison table, the uncertainty-budget table, and the two summary figures shown above.

The raw-scan fitting helper analysis/fit_from_raw.py is intentionally kept separate, because overlapping peaks and baseline drift make automated fits sensitive to the chosen time window. The repository includes analysis/windows.json so those window choices are explicit rather than hidden in the code.

Reproduce the Day 4 analysis

python -m venv .venv
pip install -r analysis/requirements.txt
python analysis/recompute_tables_day4.py

Generated outputs:

• results/day4_tableII_compare.csv
• results/day4_tableIII_error_budget.csv
• results/day4_summary.json
• results/research_snapshot.png
• results/day4_shift_summary.png
• results/day4_uncertainty_breakdown.png

Optional raw-scan refit:

python analysis/fit_from_raw.py --batch data/hd/day4_new_lamp --windows analysis/windows.json --plot

Repository structure

analysis/  Python scripts for table recomputation and raw-scan fitting
data/      Mercury calibration scans, H-D scans, and metadata
results/   Generated tables, JSON summaries, and diagnostic figures
report/    Final PDF report and LaTeX source
notes/     Lab notebook export